Unit tests for FFT implementation (replacement for gsl_fft) More...

#include <gtest/gtest.h>
#include <cmath>
#include <complex>
#include <vector>
#include "Utilities/GSLFFT.h"

Include dependency graph for TestFFT.cpp:

Classes
class	FFTTest

Functions
	TEST_F (FFTTest, ComplexFFT_Identity)

	TEST_F (FFTTest, RealFFT_Transform)

	TEST_F (FFTTest, ComplexFFT_Forward)

	TEST_F (FFTTest, ComplexFFT_Inverse)

	TEST_F (FFTTest, FFT_InverseRoundTrip)

	TEST_F (FFTTest, Radix2Forward)

	TEST_F (FFTTest, Radix2Inverse)

Detailed Description

Unit tests for FFT implementation (replacement for gsl_fft)

This file contains unit tests for GSL-compatible Fast Fourier Transform (FFT) implementations. The implementation uses the Cooley-Tukey algorithm for computing FFTs of real and complex data.

Test:: FFTTest::ComplexFFT_Identity Tests FFT of a constant signal. Verifies basic FFT functionality for complex data. A constant signal should transform to a DC component in the frequency domain.

Test:: FFTTest::RealFFT_Transform Tests forward FFT for real-valued data. Verifies that real input data is correctly transformed to the frequency domain using the GSL-compatible packed format, where the result is stored as \([r_0, r_1, i_1, r_2, i_2, \ldots]\).

Test:: FFTTest::ComplexFFT_Forward Tests forward FFT for complex data. Verifies that a unit impulse (delta function at \(n=0\)) transforms to a constant in the frequency domain (all components equal to 1).

Test:: FFTTest::ComplexFFT_Inverse Tests inverse FFT for complex data. Verifies that a constant in the frequency domain transforms back to an impulse in the time domain, confirming the inverse relationship between forward and inverse transforms.

Test:: FFTTest::FFT_InverseRoundTrip Tests round-trip FFT operations (forward followed by inverse). Verifies that applying forward FFT followed by inverse FFT recovers the original signal (within scaling factor \(N\)), confirming the mathematical relationship: \(\text{IFFT}(\text{FFT}(x)) = N \cdot x\).

Test:: FFTTest::Radix2Forward Tests radix-2 FFT algorithm for power-of-2 sized data. Verifies that the radix-2 implementation correctly computes FFTs for data sizes that are powers of 2, which allows for optimized computation.

Test:: FFTTest::Radix2Inverse Tests radix-2 inverse FFT algorithm. Verifies that the inverse radix-2 transform correctly recovers time-domain signals from frequency-domain representations.

Definition in file TestFFT.cpp.